Extended Generalized Fibonacci and Tribonacci Polynomials with some Properties - Billore, Vaishali; Patel, Naresh; Makwana, Hemant (Sarajevo Journal of Mathematics, 2025)
In this paper, we introduced the extended generalized Fibonacci polynomial sequence {Y_2,n} and extended generalized Tribonacci polynomial {Y_3,n} with arbitrary initial values and established a recursive matrix and then presented some properties of these. Further, we investigated some well-known identities like Binet's formula, Catalan's identity, Cassini's identity, d'Ocagne's identity, generating function, explicit sum formula, sum of first n terms for the extended generalized Fibonacci polynomial sequence and extended generalized Tribonacci polynomial sequence.